Hydrogen-bonding interactions often make substantial contributions to the specificity of protein-nucleic acid complexes. Using a geometric modeling approach, we previously identified 28 possible doubly hydrogen-bonded interactions to the four unpaired RNA bases. Here we present interaction energies of these models, calculated by ab initio quantum chemical methods, and describe a correlation between the computed energies and observed frequencies of the interactions. In general, interactions with charged side chains show the most favorable energies. An Asp/Glu-G interaction may be especially favorable for recognition of unpaired guanines in RNAs. Asn and Ser/Thr/Tyr side chains are calculated to make iso-energetic interactions to the Hoogsteen face of adenine, but Asn-A interactions are much more common with DNA than RNA, and Ser/Thr/Tyr-A interactions are more common with RNA than DNA. Examination of the known interactions suggests that Ser/Thr/Tyr may be accommodated in a wider variety of protein contexts at RNA-protein interfaces. With these calculated intrinsic affinities, it should be possible to better assess the contributions of bidentate hydrogen-bonding interactions to RNA- and DNA-binding specificity.